The current development of high-integrity product lines threatens to outstrip existing tools for product-line verification. Software Fault Tree Analysis (SFTA) is a technique that has been used successfully to investigate contributing causes to potential hazards in safety-critical applications. This paper adapts SFTA to product lines of systems. The contribution is to define: (1) the technique to construct a product-line SFTA and (2) the pruning technique required to reuse the SFTA for the analysis of a new system in the product line. The paper describes how product-line SFTA integrates with forward-analysis techniques such as Software Failure Modes, Effects, and Criticality Analysis (SFMECA), supports requirements evolution, and helps identify previously unforeseen constraints on the systems to be built. Applications to two small examples are used to illustrate the technique.